{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bayes' original thought experiment\n",
    "=="
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.stats as sp\n",
    "import pylab as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define the prior parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "alpha = 1\n",
    "beta = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define the set of r values (position of the line), for plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "r_vals = np.linspace(0,1,100)[:,None]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the prior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1062f4210>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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yksnJyRE/hiRJu4/p6Wmmp6cf0rZ58+ZFea90Ryx2sHN3yOM+4A+ran1f+8eA5VX1sm2M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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1061b40d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pylab as plt\n",
    "%matplotlib inline\n",
    "plt.plot(r_vals,sp.beta.pdf(r_vals,alpha,beta))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define some observations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Either define the array, or just enter the counts\n",
    "X = np.array([0,1,0,0,0,1,0,0,1,0,0,1,0,0,0,0,0])\n",
    "n_left = (X==1).sum()\n",
    "n_right = (X==0).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the prior and posterior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x106793650>]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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SgTFBHGv47kgIsCJ3BWe1PEsrTUaYRrUaMbTDUNJXp3sdRUSkUiUEc5CZPQlc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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106793750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(r_vals,sp.beta.pdf(r_vals,alpha,beta))\n",
    "plt.plot(r_vals,sp.beta.pdf(r_vals,alpha+n_left,beta+n_right))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
